{"id":"https://openalex.org/W2070857483","doi":"https://doi.org/10.1090/s0025-5718-04-01640-0","title":"Determining the 2-Sylow subgroup of an elliptic curve over a finite field","display_name":"Determining the 2-Sylow subgroup of an elliptic curve over a finite field","publication_year":2004,"publication_date":"2004-03-04","ids":{"openalex":"https://openalex.org/W2070857483","doi":"https://doi.org/10.1090/s0025-5718-04-01640-0","mag":"2070857483"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-04-01640-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01640-0","pdf_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01640-0/S0025-5718-04-01640-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01640-0/S0025-5718-04-01640-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056214875","display_name":"Josep M. Miret","orcid":"https://orcid.org/0000-0003-4631-4294"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. Miret","raw_affiliation_strings":["Department de Matem\u00c3\u00a0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","Department de Matem\u00e0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain"],"affiliations":[{"raw_affiliation_string":"Department de Matem\u00c3\u00a0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]},{"raw_affiliation_string":"Department de Matem\u00e0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075780050","display_name":"R. Pe\u00f1a-Moreno","orcid":"https://orcid.org/0000-0002-9971-7444"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"R. Moreno","raw_affiliation_strings":["Department de Matem\u00c3\u00a0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","Department de Matem\u00e0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain"],"affiliations":[{"raw_affiliation_string":"Department de Matem\u00c3\u00a0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]},{"raw_affiliation_string":"Department de Matem\u00e0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070972289","display_name":"Anna Rio","orcid":"https://orcid.org/0000-0003-4785-8760"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Rio","raw_affiliation_strings":["Departament de Matem\u00c3\u00a0tica Aplicada II, Universitat Polit\u00c3\u00a8cnica de Catalunya, Pau Gargallo 5, 08028-Barcelona, Spain","Departament de Matem\u00e0tica Aplicada II, Universitat Polit\u00e8cnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00c3\u00a0tica Aplicada II, Universitat Polit\u00c3\u00a8cnica de Catalunya, Pau Gargallo 5, 08028-Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada II, Universitat Polit\u00e8cnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain#TAB#","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030020799","display_name":"Magda Valls","orcid":"https://orcid.org/0000-0003-1992-146X"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Valls","raw_affiliation_strings":["Department de Matem\u00c3\u00a0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","Department de Matem\u00e0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain"],"affiliations":[{"raw_affiliation_string":"Department de Matem\u00c3\u00a0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]},{"raw_affiliation_string":"Department de Matem\u00e0tica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5056214875"],"corresponding_institution_ids":["https://openalex.org/I15766328"],"apc_list":null,"apc_paid":null,"fwci":4.8474,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.94975276,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"74","issue":"249","first_page":"411","last_page":"427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sylow-theorems","display_name":"Sylow theorems","score":0.8438414335250854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8328076601028442},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.7193339467048645},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.614607036113739},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5740135312080383},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5005285739898682},{"id":"https://openalex.org/keywords/hessian-form-of-an-elliptic-curve","display_name":"Hessian form of an elliptic curve","score":0.47926685214042664},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.461424857378006},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.4337219297885895},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41897082328796387},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.3339725136756897},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3255695700645447},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3005342483520508},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2923736870288849},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25122392177581787},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.1345139741897583}],"concepts":[{"id":"https://openalex.org/C124535231","wikidata":"https://www.wikidata.org/wiki/Q1057919","display_name":"Sylow theorems","level":4,"score":0.8438414335250854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8328076601028442},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.7193339467048645},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.614607036113739},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5740135312080383},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5005285739898682},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.47926685214042664},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.461424857378006},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.4337219297885895},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41897082328796387},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.3339725136756897},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3255695700645447},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3005342483520508},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2923736870288849},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25122392177581787},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.1345139741897583},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-04-01640-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01640-0","pdf_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01640-0/S0025-5718-04-01640-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.105.1196","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.1196","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2005-74-249/S0025-5718-04-01640-0/S0025-5718-04-01640-0.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-04-01640-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01640-0","pdf_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01640-0/S0025-5718-04-01640-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2070857483.pdf","grobid_xml":"https://content.openalex.org/works/W2070857483.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1486898453","https://openalex.org/W1507575253","https://openalex.org/W1803405874","https://openalex.org/W1808634574","https://openalex.org/W1846216834","https://openalex.org/W2098377074","https://openalex.org/W2100142304","https://openalex.org/W2585863193","https://openalex.org/W2728371637","https://openalex.org/W4242800324","https://openalex.org/W4292027090"],"related_works":["https://openalex.org/W3138493780","https://openalex.org/W2548082687","https://openalex.org/W3172172454","https://openalex.org/W3211097549","https://openalex.org/W1921672120","https://openalex.org/W3003881355","https://openalex.org/W1851253658","https://openalex.org/W2559355736","https://openalex.org/W2121110380","https://openalex.org/W74147110"],"abstract_inverted_index":{"In":[0],"this":[1,61,113],"paper":[2],"we":[3,43],"describe":[4],"an":[5,33],"algorithm":[6,62,87],"that":[7,55,92],"outputs":[8],"the":[9,12,17,50,58,77,98,107,116],"order":[10],"and":[11],"structure,":[13],"including":[14],"generators,":[15],"of":[16,32,49,60,64,71,83,94,103,118],"<inline-formula":[18],"content-type=\"math/mathml\">":[19],"<mml:math":[20],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[21],"alttext=\"2\">":[22],"<mml:semantics>":[23],"<mml:mn>2</mml:mn>":[24],"<mml:annotation":[25],"encoding=\"application/x-tex\">2</mml:annotation>":[26],"</mml:semantics>":[27],"</mml:math>":[28],"</inline-formula>":[29],"-Sylow":[30],"subgroup":[31],"elliptic":[34,99],"curve":[35,100],"over":[36],"a":[37,68,80],"finite":[38,108],"field.":[39,109],"To":[40],"do":[41,44],"this,":[42],"not":[45],"assume":[46],"any":[47],"knowledge":[48],"group":[51],"order.":[52],"The":[53,86],"results":[54],"lead":[56],"to":[57,75],"design":[59],"are":[63],"inductive":[65],"type.":[66],"Then":[67],"right":[69],"choice":[70],"points":[72,96],"allows":[73],"us":[74],"reach":[76],"end":[78],"within":[79],"linear":[81],"number":[82],"successive":[84],"halvings.":[85],"works":[88],"with":[89],"abscissas,":[90],"so":[91],"halving":[93],"rational":[95],"in":[97,106],"becomes":[101],"computing":[102],"square":[104],"roots":[105],"Efficient":[110],"methods":[111],"for":[112],"computation":[114],"determine":[115],"efficiency":[117],"our":[119],"algorithm.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}